Lower bounds for a conjecture of Erdős and Turán
Volume 159 / 2013
Acta Arithmetica 159 (2013), 301-313
MSC: Primary 11B13, 11B34.
DOI: 10.4064/aa159-4-1
Abstract
We study representation functions of asymptotic additive bases and more general subsets of $\mathbb N$ (sets with few nonrepresentable numbers). We prove that if $\mathbb N\setminus (A+A)$ has sufficiently small upper density (as in the case of asymptotic bases) then there are infinitely many numbers with more than five representations in $A+A$, counting order.
